A375415 Expansion of e.g.f. exp(-x^3 * (1 - x)^2) / (1 - x).
1, 1, 2, 0, 48, 120, 1080, -2520, 100800, 120960, 6652800, -26611200, 1297296000, -778377600, 177989011200, -610248038400, 53004401049600, -62245299916800, 12760286482944000, -13009267682611200, 5173295797942272000, 3608804645462016000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3*(1-x)^2)/(1-x))) -
PARI
a(n) = (-1)^n*n!*sum(k=0, n\3, binomial(2*k-1, n-3*k)/k!);
Formula
a(n) = (-1)^n * n! * Sum_{k=0..floor(n/3)} binomial(2*k-1,n-3*k)/k!.